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A closely related model, the Erdős–Rényi model denoted G(n,M), assigns equal probability to all graphs with exactly M edges. With 0 ≤ M ≤ N, G(n,M) has <math>\tbinom{N}{M}</math> elements and every element occurs with probability <math>1/\tbinom{N}{M}</math>.  The latter model can be viewed as a snapshot at a particular time (M) of the random graph process <math>\tilde{G}_n</math>, which is a stochastic process that starts with n vertices and no edges, and at each step adds one new edge chosen uniformly from the set of missing edges.

A closely related model, the Erdős–Rényi model denoted G(n,M), assigns equal probability to all graphs with exactly M edges. With 0 ≤ M ≤ N, G(n,M) has <math>\tbinom{N}{M}</math> elements and every element occurs with probability <math>1/\tbinom{N}{M}</math>.  The latter model can be viewed as a snapshot at a particular time (M) of the random graph process <math>\tilde{G}_n</math>, which is a stochastic process that starts with n vertices and no edges, and at each step adds one new edge chosen uniformly from the set of missing edges.

一个密切相关的模型，Erdős-Rényi模型表示''G'' (''n'',''M'')，给每一个正好有''M''条边的图赋予等概率。当0≤ ''M'' ≤ ''N'' 时，''G'' (''n'',''M'')具有 <math>\tbinom{N}{M}</math> 元素，且每个元素都以概率<math>1/\tbinom{N}{M}</math> 出现。后一个模型可以看作是随机图过程<math>\tilde{G}_n</math>某个特定时间(''M'')的一个快照，这个时间(''M'')是从 n 个顶点开始没有边的一个随机过程，每个步骤均匀地从缺失的边集中选择一个新的边。

一个相关性强的模型，Erdős-Rényi模型表示''G'' (''n'',''M'')，给每一个正好有''M''条边的图赋予等概率。当0≤ ''M'' ≤ ''N'' 时，''G'' (''n'',''M'')具有 <math>\tbinom{N}{M}</math> 元素，且每个元素都以概率<math>1/\tbinom{N}{M}</math> 出现。后一个模型可以看作是随机图过程<math>\tilde{G}_n</math>某个特定时间(''M'')的一个快照，这个时间(''M'')是从 n 个顶点开始没有边的一个随机过程，每个步骤均匀地从缺失的边集中选择一个新的边。

If instead we start with an infinite set of vertices, and again let every possible edge occur independently with probability 0 < p < 1, then we get an object G called an infinite random graph. Except in the trivial cases when p is 0 or 1, such a G almost surely has the following property:

If instead we start with an infinite set of vertices, and again let every possible edge occur independently with probability 0 < p < 1, then we get an object G called an infinite random graph. Except in the trivial cases when p is 0 or 1, such a G almost surely has the following property:

如果我们从一个无限的顶点集合开始，然后再次让每个可能的边以概率0 < ''p'' < 1独立出现，那么我们得到一个对象 ''G'' 称为'''<font color="#FF8000">无限随机图 Infinite Graph </font>'''。除了在 ''p'' = 0或1的平凡情况下，这样的 ''G'' 几乎肯定具有以下性质:

如果我们从一个无限的顶点集合开始，然后再次让每个可能的边以概率0 < ''p'' < 1独立出现，那么我们得到一个对象 ''G'' 称为'''<font color="#FF8000">无限随机图 Infinite Graph </font>'''。除了在 ''p'' = 0或1的平凡情况下，这样的 ''G'' 在大多数情况下肯定具有以下性质:

For M ≃ pN, where N is the maximal number of edges possible, the two most widely used models, G(n,M) and G(n,p), are almost interchangeable.

For M ≃ pN, where N is the maximal number of edges possible, the two most widely used models, G(n,M) and G(n,p), are almost interchangeable.

对于 ''M''something ''pN''，其中 ''N'' 是可能的最大边数，两个最广泛使用的模型，''G'' (''n'',， ''M'')和 ''G'' (''n''，''p'')是几乎可互换的。

对于 ''M''something ''pN''，其中 ''N'' 是可能的最大边数，两个最广泛使用的模型，''G'' (''n'',， ''M'')和 ''G'' (''n''，''p'')在大多数情况下是可互换的。